Pile Design and Construction Practice, Fifth edition

The natural frequency of the member is given by the equation:
fN � K�
L2�EI M
(8.13)
where K� is a constant, L is the pile length, E is the elastic modulus, I is the moment of
inertia, and M is the effective mass per unit length of pile. W s should take into account
the possibility of barnacle growth. K� is equal to 0.56, 2.45 and 3.56 respectively for cantilevered,
propped, and fully fixed piles. The elastic modulus is expressed in units of
force. In the case of a cylindrical pile the effective mass M is equal to the mass of
the pile material plus the mass of water displaced by the pile. Where hollow tubular
piles are filled with water the mass of the enclosed water must be added to the mass of
the material. In the case of a tubular steel pile with a relatively thin wall the effective
mass is approximately equal to the mass of the steel plus twice the mass of the displaced
water.
BS 6349 provides graphs relating V crit in equation 8.12 to L�/W s where L� is the overall pile
length from deck level, where the pile is assumed to be pin-jointed, to the level of apparent
fixity below sea bed.
Very severe oscillations were experienced during the construction of the Immingham Oil
Terminal. At this site in the Humber Estuary, piles were driven through water with a mean
depth of 23 m and where ebb currents reach a mean velocity of 2.6 m/s (5 knots). The piles
were helically welded steel tubes with outside diameters of 610 mm and 762 mm and a wall
thickness of 12.7 mm. Before the piles could be braced together they developed a cross-flow
motion which at times had an amplitude of �1.2 m. Many of the piles broke off at or above
the sea bed. A completed dolphin consisting of a cap block with a mass of 700 tonnes
supported by 17 piles swayed with a frequency of 90 cycles per minute and an amplitude
of �6 mm.
Moored ships can transmit forces due to current drag onto the piles supporting the mooring
bollards. The current drag on the ship is calculated from equation 8.10.
8.1.5 Wind forces on piles
Wind forces exerted directly on piles in a jetty structure are likely to be small in relation
to the quite substantial wind forces transmitted to the piles from deck beams,
cranes, conveyors, stacked, containers, sheds and pipe trunkways. In a jetty approach
the combined wind and wave forces which usually act perpendicularly to the axis of the
approach can cause large overturning moments on the pile bents, particularly when the
wind forces are acting on pipe trunkways or conveyor structures placed at a high elevation,
say at a location with a high tidal range. Wind forces on moored ships also require
consideration, and allowance should be made where necessary for the accretion of ice
on structures.
Wind forces can be calculated from equation 8.10 by taking the mass of air as 1.29 g/l or
this equation can be conveniently expressed in Imperial units as
F � 0.00256V 2 C DA
Piling for marine structures 413
(8.14)